Following many long hours of research, I believe that I have found a good option for our Zynq board: the KRM-3Z45-768-B from Knowledge Resources. It provides a Zynq XC7Z045 (900 DSP slices) and can be mounted on a well-designed carrier board. Most importantly, it can be complemented by two KR-HDMI-A1 HDMI out modules, which could be used to drive our two touchscreens.
I wish that I could have found a board for the Zynq XC7Z100, but the only ones available are the Zynq MMP, which does not provide enough I/Os, the Mini-ITX, which is too large, or the proFPGA uno, which is too expensive ($8,600). That being said, this is only a temporary option until we upgrade to a Zynq UltraScale+ board (none available to date).
There are a few more reasons why I like the KRM board: first, it comes with a large heat spreader, which is much better than a fan (no noise, smaller form factor); second, Knowledge Resources provides think tank services, which could prove highly valuable if we hit some roadblock.